If you want to save some seeds it's recommended to ferment them in their own juice and some water until a moldy scum forms on top of the bowl (4 to 5 days), to dissolve the gel around the seed and to create an acidic condition that will kill bacteria, mold, etc. Then rinse and dry them well and store in a cool dry place.
If you simply want to grow them now there's really no need to do this. I've had fresh tomato seeds grow just squeezed from the fresh fruit into soil.
My old time relatives always dried them on paper towels or cardboard and they did fine that way.
I would go the fermentation route to kill off any possible pathogens first, and plant 'em, but I'll bet they'll grow any way you do it.

Instead of using paper towels, consider using a paper coffee filter if you have one handy, they do not come apart and stick to the dried seeds like a paper towel does.

I have had tomato plants growing from within a tomato, sooo as TreeFrog stated, you can simply start the seeds right from the tomato itself, no washing, no nothing, just do it.

good luck

Thanks for the advice - I'm going to get started!